Powers of the Vertex Cover Ideal of a Chordal Graph

DOI10.1080/00927872.2010.512582zbMath1236.13001OpenAlexW2048351607MaRDI QIDQ3113829

Fatemeh Mohammadi

Publication date: 25 January 2012

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927872.2010.512582

zbMATH Keywords

chordal graphscomponentwise linear resolutionvertex cover algebra

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Graded rings (13A02)

Related Items

Powers of componentwise linear ideals: the Herzog-Hibi-Ohsugi conjecture and related problems ⋮ Rooted order on minimal generators of powers of some cover ideals ⋮ Strong shellability of simplicial complexes ⋮ Two lower bounds for the Stanley depth of monomial ideals ⋮ Toric rings arising from vertex cover ideals ⋮ Shedding vertices and ass-decomposable monomial ideals ⋮ Componentwise linearity of powers of cover ideals ⋮ Powers of vertex cover ideals of simplicial trees ⋮ Powers of ideals associated to \((C_{4},2K_{2})\)-free graphs ⋮ Powers of the vertex cover ideals ⋮ On the powers of vertex cover ideals ⋮ Symbolic powers of vertex cover ideals ⋮ The Behaviors of Expansion Functor on Monomial Ideals and Toric Rings

Cites Work

• On rigid circuit graphs
• Ideals with linear quotients
• Four counterexamples in combinatorial algebraic geometry
• Componentwise linear ideals and Golod rings
• Dirac's theorem on chordal graphs and Alexander duality
• Rigid resolutions and big Betti numbers
• Cohen--Macaulay chordal graphs
• The depth of powers of an ideal
• Sequentially Cohen-Macaulay edge ideals
• Decompositions of Simplicial Complexes Related to Diameters of Convex Polyhedra
• Shellable nonpure complexes and posets. II
• Shellable Nonpure Complexes and Posets. I